Power-law connections: From Zipf to Heaps and beyond

Journal Article · Wed May 15 04:00:00 EDT 2013 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2013.01.013· OSTI ID:22220712

In this paper we explore the asymptotic statistics of a general model of rank distributions in the large-ensemble limit; the construction of the general model is motivated by recent empirical studies of rank distributions. Applying Lorenzian, oligarchic, and Heapsian asymptotic analyses we establish a comprehensive set of closed-form results linking together rank distributions, probability distributions, oligarchy sizes, and innovation rates. In particular, the general results reveal the fundamental underlying connections between Zipf’s law, Pareto’s law, and Heaps’ law—three elemental empirical power-laws that are ubiquitously observed in the sciences. -- Highlights: ► The large-ensemble asymptotic statistics of rank distributions are explored. ► Lorenzian, oligarchic, and Heapsian asymptotic analyses are applied. ► Associated oligarchy sizes and induced innovation rates are analyzed. ► General elemental statistical connections are established. ► The underlying connections between Zipf’s, Pareto’s and Heaps’ laws are unveiled.

• OSTI ID: 22220712
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Vol. 332; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
DISTRIBUTION
PHASE TRANSFORMATIONS
PROBABILITY
STATISTICS